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Question Number 196688 Answers: 1 Comments: 0

Question Number 196683 Answers: 2 Comments: 0

If y = ((e^x − e^(− x) )/(e^x + e^(− x) )) then show that x = (1/2)log_e (((1 + y)/(1 − y))).

$$\mathrm{If}\:{y}\:=\:\frac{{e}^{{x}} \:−\:{e}^{−\:{x}} }{{e}^{{x}} \:+\:{e}^{−\:{x}} }\:\mathrm{then}\:\mathrm{show}\:\mathrm{that} \\ $$$${x}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}_{{e}} \left(\frac{\mathrm{1}\:+\:{y}}{\mathrm{1}\:−\:{y}}\right). \\ $$

Question Number 196682 Answers: 1 Comments: 0

Question Number 196672 Answers: 1 Comments: 1

Find all Ω=abcdef ^(−) , such that abcdef=abc+def

$${Find}\:{all}\:\Omega\overline {={abcdef}\:\:},\:{such}\:{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{abcdef}={abc}+{def} \\ $$

Question Number 196676 Answers: 1 Comments: 1

If ab^(−) ∙ cd^(−) =899 , find Ω= abcd^(−) + cdab^(−)

$${If}\:\overline {{ab}}\:\centerdot\:\overline {{cd}}=\mathrm{899}\:,\:{find}\:\Omega=\:\overline {{abcd}}\:+\:\overline {{cdab}} \\ $$

Question Number 196674 Answers: 0 Comments: 0

prove that lim_(n→+∞) (−1)^(n−1) +Σ_(p=2) ^n (−1)^p pln(((p+1)/(p−1)))=ln(π)

$$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\:\left(−\mathrm{1}\right)^{\mathrm{n}−\mathrm{1}} +\underset{\mathrm{p}=\mathrm{2}} {\overset{\mathrm{n}} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{p}} \mathrm{pln}\left(\frac{\mathrm{p}+\mathrm{1}}{\mathrm{p}−\mathrm{1}}\right)=\mathrm{ln}\left(\pi\right) \\ $$

Question Number 196667 Answers: 3 Comments: 0

Question Number 196663 Answers: 0 Comments: 0

Question Number 196659 Answers: 4 Comments: 4

Question Number 196657 Answers: 0 Comments: 0

A pilot flies his plane directly from a point A to a point B, a distance of 450Km. The bearing of B from A is 030°. A wind of 80Km/hr is blowing from the east. Given that the plane can travel at 320Km/hr in still air. Find (i) The bearing on which the plane must be steered. (ii) The time taken to fly from A to B.

$$\mathrm{A}\:\mathrm{pilot}\:\mathrm{flies}\:\mathrm{his}\:\mathrm{plane}\:\mathrm{directly}\:\mathrm{from}\:\mathrm{a}\:\mathrm{point}\:\mathrm{A}\:\mathrm{to}\:\mathrm{a}\:\mathrm{point}\:\mathrm{B}, \\ $$$$\mathrm{a}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{450Km}.\:\mathrm{The}\:\mathrm{bearing}\:\mathrm{of}\:\mathrm{B}\:\mathrm{from}\:\mathrm{A}\:\mathrm{is}\:\mathrm{030}°.\:\mathrm{A} \\ $$$$\mathrm{wind}\:\mathrm{of}\:\mathrm{80Km}/\mathrm{hr}\:\mathrm{is}\:\mathrm{blowing}\:\mathrm{from}\:\mathrm{the}\:\mathrm{east}.\:\mathrm{Given}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{plane}\:\mathrm{can}\:\mathrm{travel}\:\mathrm{at}\:\mathrm{320Km}/\mathrm{hr}\:\mathrm{in}\:\mathrm{still}\:\mathrm{air}.\:\mathrm{Find}\: \\ $$$$\left(\mathrm{i}\right)\:\mathrm{The}\:\mathrm{bearing}\:\mathrm{on}\:\mathrm{which}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{must}\:\mathrm{be}\:\mathrm{steered}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{The}\:\mathrm{time}\:\mathrm{taken}\:\mathrm{to}\:\mathrm{fly}\:\mathrm{from}\:\mathrm{A}\:\mathrm{to}\:\mathrm{B}. \\ $$

Question Number 196652 Answers: 2 Comments: 0

solve 3x^(3/2) −4x^(1/2) +1=0

$${solve} \\ $$$$\mathrm{3}{x}^{\frac{\mathrm{3}}{\mathrm{2}}} \:−\mathrm{4}{x}^{\frac{\mathrm{1}}{\mathrm{2}}} \:+\mathrm{1}=\mathrm{0} \\ $$

Question Number 196650 Answers: 2 Comments: 0

Prove that x^3 =y^6 +20 has no positive integer solution.

$$\mathrm{Prove}\:\mathrm{that}\:{x}^{\mathrm{3}} ={y}^{\mathrm{6}} +\mathrm{20}\:\mathrm{has}\:\mathrm{no}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{solution}. \\ $$

Question Number 196648 Answers: 0 Comments: 0